(a) Work out the third even-parity normalized energy eigenstate of the simple harmonic ocillator in 1 dimension,for a particle of mass m, spring frequency w, .i.e. the n = 4 state in the position representation. Plot it and confirm that it has 4 nodes. (b) Graphically compare its probability density with the classical result for this quantity in a Newtonian state having the same energy.

(a) Work out the third even-parity normalized energy eigenstate of the simple harmonic ocillator in 1 dimension,for a particle of mass m, spring frequency w, .i.e. the n = 4 state in the position representation. Plot it and confirm that it has 4 nodes. (b) Graphically compare its probability density with the classical result for this quantity in a Newtonian state having the same energy.